Pseudo-Almost Periodic Solutions in the Alpha-Norm and in Stepanov’s Sense for some Evolution Equations

Our aim is to introduce the concept of double-measure ergodic and double-measure pseudo-almost periodic functions in Stepanov’s sense. In addition, we present numerous interesting results, such as the composition theorems and completeness properties, for these two spaces of considered functions. We also establish the existence and uniqueness for double-measure pseudo-almost periodic mild solutions in Stepanov’s sense for some evolution equations.